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Asteroid Systems: Binaries, Triples, and Pairs

Jean-Luc MargotUniversity of California, Los Angeles

Petr PravecAstronomical Institute of the Czech Republic Academy of Sciences

Patrick TaylorArecibo Observatory

Benoıt CarryInstitut de Mecanique Celeste et de Calcul desEphemerides

Seth JacobsonCote d’Azur Observatory

In the past decade, the number of known binary near-Earth asteroids has morethan quadrupled and the number of known large main belt asteroids with satelliteshas doubled. Half a dozen triple asteroids have been discovered, and the previouslyunrecognized populations of asteroid pairs and small main belt binaries havebeen identified. The current observational evidence confirms that small (.20 km)binaries form by rotational fission and establishes that theYORP effect powers thespin-up process. A unifying paradigm based on rotational fission and post-fissiondynamics can explain the formation of small binaries, triples, and pairs. Large (&20km) binaries with small satellites are most likely created during large collisions.

1. INTRODUCTION

1.1. Motivation

Multiple-asteroid systems are important be-cause they represent a sizable fraction of the aster-oid population and because they enable investiga-tions of a number of properties and processes thatare often difficult to probe by other means. Thebinaries, triples, and pairs inform us about a greatvariety of asteroid attributes, including physicalproperties, composition, interior structure, for-mation processes, and evolutionary processes.

Observations of binaries and triples provide themost powerful way of deriving reliable massesand densities for a large number of objects. Thedensity measurements help us understand the

composition and internal structure of minor plan-ets. Binary systems offer opportunities to mea-sure thermal and mechanical properties, whichare generally poorly known.

The binary and triple systems within near-Earth asteroids (NEAs), main belt asteroids(MBAs), and trans-Neptunian objects (TNOs) ex-hibit a variety of formation mechanisms (Merlineet al. 2002c; Noll et al. 2008). As such, they pro-vide an invaluable window on accretional, colli-sional, tidal, and radiative processes that are criti-cal in planet formation. The distribution and con-figurations of the multiple-asteroid systems alsoprovide a rich array of constraints on their envi-ronment, their formation, and their evolutionarypathways.

Observations rely primarily on ground-based

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telescopes and the Hubble Space Telescope (HST).For an up-to-date list of binaries and triples in thesolar system, see Johnston (2014). We describeobservational techniques only briefly because thismaterial is available elsewhere (e.g., Merline et al.2002c). A few emerging techniques will be de-scribed in more detail. Likewise, we refer thereader to other texts for an extensive history ofthe field (e.g., Merline et al. 2002c) and highlightonly a few of the developments here.

1.2. History

Early search programs for asteroid satelliteswere unsuccessful, returning negative or dubiousresults, such that the authors of theAsteroids IIreview chapter chose the prudent title “Do as-teroids have satellites?” (Weidenschilling et al.1989). The chapter provides an excellent discus-sion of the physics of several formation mecha-nisms that were postulated at the time. The per-spective changed with the flyby of (243) Ida bythe Galileo spacecraft in 1993 and the discov-ery of its small satellite Dactyl (Chapman et al.1995; Belton et al. 1995). Ground-based effortsintensified and resulted in the discovery of a satel-lite around (45) Eugenia by Merline et al. (1999).Several other discoveries followed in rapid suc-cession. The relatively small sizes of the MBAsatellites suggested formation in sub-catastrophicor catastrophic collisions (Durda 1996; Dores-soundiram et al. 1997).

The discovery of MBA satellites, coupled withanalysis of terrestrial doublet craters (Bottke andMelosh 1996a,b) and anomalous lightcurve ob-servations (Pravec and Hahn 1997), suggested theexistence of binary asteroids in the near-Earthpopulation as well. The unambiguous detectionof five NEA binaries by radar cemented this find-ing and indicated that NEA satellites form bya spin-up and rotational fission process (Margotet al. 2002). Lightcurve observers reached thesame conclusion independently (Pravec and Har-ris 2007). Both radar and lightcurve observationsrevealed that, far from being rare, binary asteroidsare relatively common (Pravec et al. 1999; Margotet al. 2002; Pravec et al. 2006). By the time theAsteroids III review chapter was written, a more

decisive title (“Asteroids do have satellites”) hadbecome appropriate (Merline et al. 2002c). Thisreview focuses on the developments that followedthe publication ofAsteroids III.

1.3. Terminology

Two- and three-component asteroids that aregravitationally bound will be referred to asbi-nary asteroids (or binaries) and triple asteroids(or triples), respectively. (Triple is favored overthe more directly analogous termstrinary andternary because of long-established usage in as-tronomy).Asteroid pairs denote asteroid compo-nents that are genetically related but not gravita-tionally bound.Paired binaries or paired triplesare asteroid pairs where the larger asteroid is itselfa binary or triple asteroid. The larger componentin binaries, triples, and pairs is referred to as theprimary component or primary. The smaller com-ponent in binaries is referred to as thesecondarycomponent or secondary.

There has been some confusion in the literatureabout the meaning of the word “asynchronous.”Here, we adopt the terminology proposed byMargot (2010) and later implemented by Jacob-son and Scheeres (2011b) and Fang and Margot(2012c). Binaries with an absence of spin-orbitsynchronism are calledasynchronous binaries.Binaries with a secondary spin period synchro-nized to the mutual orbit period are calledsyn-chronous binaries. Binaries with both primaryand secondary spin periods synchronized to themutual orbit period are calleddoubly synchronousbinaries. If generalization to systems with morethan one satellite is needed, we affix the termssynchronous and asynchronous to the satellitesbeing considered.

It is useful to present results forsmall andlargeasteroids. We place an approximate dividing lineat the size at which objects are substantially af-fected by the YORP effect during their lifetime.For typical NEAs and MBAs, this dividing linecorresponds to a diameter of about 20 km (Jacob-son et al. 2014a). We definevery small asteroidsas those with diameters of less than 200 m. Thisis the approximate size below which many aster-oids are observed to spin faster than the disruption

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rate of a body with no shear or tensile strengthωd =

√

4πρG/3, whereρ is the density andG isthe gravitational constant.

We use two additional acronyms. The YORPeffect is a radiation-powered rotational acceler-ation mechanism for small asteroids (Rubincam2000). The binary YORP (BYORP) effect isa radiation-powered acceleration mechanism thatmay expand or contract the orbits of some syn-chronous asteroids (Cuk and Burns 2005).

2. OBSERVATIONS

Several observational techniques are availablefor discovering, detecting, and studying binaries,triples, and pairs, each with its strengths andweaknesses. This section describes recent resultsand illustrates the complementarity of the obser-vational techniques that characterize individualasteroid systems and entire populations.

2.1 Radar Observations of NEA Systems

Radar has proven to be a powerful methodof detecting secondaries to NEAs, enabling thediscovery (as of September 2014) of the satel-lites in 71% of the 49 known multiple-componentNEA systems, including 33 of 47 binaries andboth undisputed triple systems. Of the 14 bi-nary NEAs discovered via optical lightcurve tech-niques, 6 have been confirmed with follow-upradar observations during later apparitions. Over-all, radar detections suggest that about one in sixNEAs larger than 200 m in diameter are multiple-asteroid systems (Margot et al. 2002; Taylor et al.2012a), though 200 m is not a sharp cutoff. Threebinary NEA systems identified by radar have pri-mary components with suggested diameters of120 m to 180 m: 2003 SS84 (Nolan et al. 2003),(363599) 2004 FG11 (Taylor et al. 2012c), and1994 CJ1 (Taylor et al. 2014). For comparison,the largest primaries of binary NEAs imaged withradar: (5143) Heracles (Taylor et al. 2012b), thepossible triple (276049) 2002 CE26 (Shepard et al.2006), and (285263) 1998 QE2 (Springmann et al.2014), are more than an order of magnitude largerat >3 km in diameter. It is likely that∼8 kmdiameter (1866) Sisyphus has a secondary based

on analysis of frequency-only observations ob-tained on four separate dates in 1985 (Ostro, pers.comm., 2001).

Radar observations can be used to detect aster-oid satellites because of the ability to resolve thecomponents of the system both spatially (alongthe observer’s line of sight) and in terms of fre-quency (due to Doppler shifts from the rotationaland orbital line-of-sight velocities), resulting ina measurable separation between the componentsin two dimensions. Direct detection of a satel-lite in frequency-only spectra or radar images typ-ically occurs within one observing session andoften within minutes of observation. The band-width of the echo of a component scales directlywith the diameter and rotation rate. Thus, ina frequency-only experiment, the signal of thesmaller, relatively slowly rotating satellite is con-densed to a smaller bandwidth that is superim-posed upon the broadband signal of the larger, of-ten rapidly rotating, primary (Fig. 1, top). Notall radar-observed binaries present this character-istic spectrum (e.g., where the secondary spinsfaster than the synchronous rate), but all are read-ily detected in radar images when the componentsare also resolved spatially (Fig. 1, bottom). Be-cause the spatial resolution achieved with radarinstruments corresponds to an effective angularresolution of better than∼1 milliarcsecond (mas),there is no bias against the detection of satel-lites orbiting very close to the primary compo-nent. Multiple measurements of the range andfrequency separations of the components overdays of sky motion provide the geometric lever-age required to determine the orbit of the sec-ondary around the primary. This can be donefor any orbital orientation and yields the totalsystem mass, a property that is difficult to esti-mate otherwise. Other techniques involve analyz-ing spacecraft flyby and orbit trajectories (e.g.,Yeomans et al. 1999), measuring the Yarkovskyorbital drift in conjunction with thermal proper-ties (e.g., Chesley et al. 2014), or observing thegravitational perturbations resulting from asteroidencounters (e.g., Hilton 2002).

Most binary NEA systems observed to datehave a rapidly rotating primary and a smaller

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-10 -5 0 5 10Doppler frequency (Hz)

Fig. 1.— Binary near-Earth asteroid (285263) 1998QE2 as detected using the Arecibo planetary radarsystem. In the frequency-only spectrum showingecho power as a function of Doppler frequency (top),the narrowband echo of the tidally locked secondarystands out against the broadband echo of the larger,faster-rotating primary. In the radar image (bottom),the components are spatially resolved (7.5 m/pixel).The vertical axis represents distance from the observerincreasing downward. The horizontal axis is Dopplerfrequency due to the orbital and rotational motion ofthe components. Note that if one summed the pixelvalues in each column of the image, the intensity asa function of Doppler frequency would approximatethe spectrum above. The secondary is roughly one-fourth the size of the primary (measured in the verti-cal dimension), though the Doppler breadth of the pri-mary gives the illusion of a greater size disparity. Theshape of the secondary (inset) is distinctly nonspheri-cal when viewed with finer frequency resolution.

secondary of order a few tenths the size of theprimary (a secondary-to-primary mass ratio ofroughly 0.001 to 0.1), whose rotation is synchro-nized to the mutual orbit period. The majorityof primaries rotate in less than 2.8 h, thoughthey range from 2.2593 h for (65803) Didy-mos (Pravec et al. 2006) to 4.749 h for 1998QE2 (P. Pravec, pers. comm., 2013). The knownoutlier is the nearly equal-mass binary (69230)Hermes, whose components both appear to have13.894 h periods synchronized to their mutual or-bit period (Margot et al. 2006). This doubly syn-chronous configuration is most likely due to rapidtidal evolution (Taylor and Margot 2011). Whilethe rotations of satellites in NEA binaries tendto be tidally locked to their orbital mean motionswith periods typically within a factor of two of 24h (often resulting in the characteristic appearanceshown in Fig. 1), about one in four radar-observedmultiple-asteroid systems have an asynchronoussatellite (Brozovic et al. 2011), all of which ro-tate faster than their orbital rate. Well-studiedexamples include (35107) 1991 VH (Naidu et al.2012), (153958) 2002 AM31 (Taylor et al. 2013),(311066) 2004 DC (Taylor et al. 2008), and theouter satellites of both undisputed triple systems(153591) 2001 SN263 (Nolan et al. 2008; Fanget al. 2011; Becker et al. 2015) and (136617)1994 CC (Brozovic et al. 2011; Fang et al. 2011).Of the known asynchronous satellites, all havewide component separations (>7 primary radii),translating to longer-than-typical orbital periods,and/or eccentric orbits (>0.05), that are eitherremnants of their formation mechanism or prod-ucts of subsequent dynamical evolution (Fang andMargot 2012c).

The shortest orbital periods detected with radarso far are those of Didymos and 2006 GY2 withPorb = 11.90+0.03

−0.02 h and11.7 ± 0.2 h, respec-tively (Benner et al. 2010; Brooks 2006). ForDidymos, the semi-major axis isa = 1.18+0.04

−0.02 km,just outside the classical fluid Roche limit of∼1km for equal-density components. Other sys-tems with satellites orbiting near this limit include2002 CE26 and 2001 SN263. The significance ofthis limit is unclear, as∼100 m secondaries witha cohesion comparable to comet regolith or sandcan likely survive on orbits interior to the Roche

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limit (Taylor and Margot 2010, and referencestherein).

Inversion of a series of radar images can pro-vide a three-dimensional shape model and com-plete spin-state description given sufficient sig-nal, resolution, and orientational coverage (Hud-son 1993; Magri et al. 2007). Shape recon-struction of the larger component of (66391)1999 KW4 (Ostro et al. 2006) demonstrated thatthe canonical shape of an NEA primary hasa characteristic circular equatorial bulge, uni-formly sloped sides, and polar flattening akin toa spinning top. Such a shape is shared by theprimaries of 2004 DC, 1994 CC, 2001 SN263,and (185851) 2000 DP107 (Naidu et al. 2015),though some primaries have less pronouncedequatorial belts, e.g., 2002 CE26 and 1998 QE2.Some single asteroids have a similar shape,e.g., (101955) Bennu (Nolan et al. 2013) and(341843) 2008 EV5 (Busch et al. 2011), but donot have satellites, possibly because one has notyet formed or has been lost in the past. Shapemodel renditions are shown in Benner et al. (thisvolume). Often the resolution of radar imagesof the smaller satellites is insufficient for shapeinversion, but radar images suggest that the satel-lites are typically elongated, e.g., 2000 DP107,1999 KW4, 2001 SN263, 1991 VH, and 1998 QE2.

Shapes and volumes obtained from inversionof radar images, combined with the system massderived from the orbital motion observed in radarimages, provide the density of the system (or ofthe individual components if the mass ratio ismeasurable from reflex motion). Low densitiesof order 1 g/cm3 (Shepard et al. 2006; Beckeret al. 2015) to 2 g/cm3 (Ostro et al. 2006; Bro-zovic et al. 2011) suggest significant internalmacroporosity of order 50%, implying a rubble-pile internal structure for the components. Atsuch low densities, the rapid rotation of the pri-mary places particles along the equatorial beltin a near-weightless environment. The combina-tion of rapid rotation, shape, and implied porosityand rubble-pile structure has implications for theformation mechanism of small multiple-asteroidsystems (Section 4).

While radar allows for direct, unambiguous de-

tection of asteroid satellites, its range is limited.Because radar requires the transmission and re-ception of a signal, the strength of the receivedsignal falls as the fourth power of the distance tothe target and, thus, is best suited for detectingmultiple-component systems passing within∼0.2astronomical units (au) of Earth. Satellites in themain asteroid belt simply tend to be too small andtoo far away to detect with present radar capabil-ities and require application of different observa-tional techniques.

2.2 Lightcurve Observations of NEA andSmall MBA Systems

A photometric lightcurve is a time series ofmeasurements of the total brightness of an as-teroid. Detections of binary asteroids by photo-metric lightcurve observations utilize the fact thatthe components can obscure or cast a shadow onone another, producing occultations or eclipses,respectively. The attenuations can be used to bothreveal and characterize binaries (Fig. 2). Theobservational, analysis, and modeling techniqueswere described in Pravec et al. (2006); Scheirichand Pravec (2009); Scheirich et al. (2015).

Early reports (Tedesco 1979; Cellino et al.1985) of asteroids suspected to be binaries onthe basis of anomalous lightcurves (including(15) Eunomia, (39) Laetitia, (43) Ariadne, (44)Nysa, (49) Pales, (61) Danae, (63) Ausonia, (82)Alkmene, (171) Ophelia, and (192) Nausikaa)have remained largely unconfirmed despite ex-tensive follow-up searches. The first serious can-didate for detection with this technique was NEA(385186) 1994 AW1 (Pravec and Hahn 1997),whose binary nature was confirmed by photo-metric observations in 2008 (Birlan et al. 2010).Since 1997, nearly 100 binaries among near-Earthand small main belt asteroids have been detectedwith the photometric method. The binary asteroiddatabase constructed by Pravec and Harris (2007)(http://www.asu.cas.cz/∼asteroid/binastdata.htm)includes data for 86 MBA and NEA binaries thatwere securely detected by photometry and forwhich basic parameters have been derived, suchas the primary spin period, the orbital period, andthe primary-to-secondary mean diameter ratio. A

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Fig. 2.—Lightcurve data of (1338) Duponta, which has a secondary-to-primary diameter ratio of about 0.24.(a) The original data showing both lightcurve components, folded with the orbit period. (b) The orbital lightcurvecomponent, derived after subtraction of the primary lightcurve component, showing the mutual events betweencomponents of the binary system. (c) The primary lightcurvecomponent. Figure from Pravec et al. (2012).

few tens of additional MBAs and NEAs are sus-pected to be binaries and await confirmation withmore detailed observations in the future.

Among the main findings obtained from pho-tometric observations is that binary asteroids areubiquitous. They have been found among NEAs,Mars-crossers (MCs), and throughout the mainbelt, both among asteroids that have been identi-fied as family members and among asteroids thathave not. Pravec et al. (2006) derived the fractionof binaries among NEAs larger than 300 metersto be15 ± 4%. A binary fraction among MBAshas not been derived precisely due to less well-characterized observational selection effects, buttheir photometric discovery rate is similar to thediscovery rate of binaries among NEAs. Thus,binaries are suspected to be as frequent amongMBAs as they are among NEAs. There appears

to be an upper limit on the primary diameter forphotometrically detected binaries of about 13 km;the largest detected binary is (939) Isberga withDp = 13.4± 1.3 km (Carry et al. 2015). A lowersize limit on the primary diameterDp is less clear.The smallest detected binary is 2000 UG11 withDp = 0.26 ± 0.03 km (Pravec et al. 2006), butsmaller binaries are known to exist (Section 2.1).Their absence in lightcurve data sets may be duein part to a bias against detecting small binaries inthe initial surveys.

Another key finding is that small binary aster-oids have, with only two or three exceptions, anear-critical angular momentum content (Fig. 3).As shown by Pravec and Harris (2007), their an-gular momentum is consistent with formation byfission of critically spinning parent bodies of a co-hesionless, rubble pile structure. The exceptions

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Fig. 3.— Estimated values of the normalized totalangular momentum content of binaries versus primarydiameter. The quantityαL is the sum of orbital andspin angular momenta normalized by the angular mo-mentum of an equivalent sphere spinning at the criti-cal disruption spin rateωd =

√

4πρG/3 whereρ isthe density andG is the gravitational constant. In theDarwin notation,αL = 1 corresponds toJ/J ′ = 0.4.Group A contains small NEA, MC, and MBA binaries.Group B consists of doubly synchronous small MBAswith nearly equal-size components. Group L repre-sents large MBAs with small satellites (Section 2.5).Two exceptional cases are the doubly synchronous as-teroids (90) Antiope and (617) Patroclus (Section 2.5).Figure updated from Pravec and Harris (2007).

are the semi-wide systems (32039) 2000 JO23 and(4951) Iwamoto, and possibly also (1717) Arlon,with orbital periods of 117 h to 360 h and super-critical total angular momentum content.

The orbital poles of main belt binaries werefound to have a highly anisotropic distribution,concentrating within 30 degrees of the poles ofthe ecliptic (Pravec et al. 2012). The preferen-tial orientations of the orbital poles suggest that

their parent bodies or the primaries were tiltedby the YORP effect towards the asymptotic spinstates near obliquities 0 and 180 degrees, consis-tent with observations of single asteroids (Hanuset al. 2011).

Another significant finding is that there ap-pears to be a lower limit on the separation be-tween components of binary systems of abouta/Dp = 1.5, corresponding to an orbital period of11–12 h for typical densities. Lightcurve observa-tions indicate that the orbital period of Didymosis Porb = 11.91 ± 0.02 h (Pravec et al. 2006),consistent with the radar estimate. This suggestsan orbit close to the Roche limit for strengthlesssatellites (but see prior remark about orbits inte-rior to the Roche limit).

Photometric observations of a binary systemover multiple apparitions can be used to detecta change in the separation of the componentsdue to the effect on mutual event timing. Anextensive set of photometric observations of thesynchronous binary (175706) 1996 FG3 obtainedduring 1996-2013 places an upper limit on thedrift of its semi-major axis that is one order ofmagnitude less than estimated on the basis of theBYORP theory (Scheirich et al. 2015). This sys-tem may be in an equilibrium between BYORPand tidal torques as proposed for synchronous bi-nary asteroids by Jacobson and Scheeres (2011a).

Some data sets strongly suggest the presence oftriple asteroids. In these cases, an additional rota-tional component that does not belong to the pri-mary or the close eclipsing secondary is presentin the lightcurve. This additional rotational com-ponent does not disappear during mutual eventswhere the eclipsing close secondary is obscuredby or in the shadow of the primary. Pravec et al.(2012) identified three such cases: (1830) Pog-son, (2006) Polonskaya, and (2577) Litva. Thelatter has been confirmed by direct imaging ob-servations of the third body (second satellite) ona wide orbit (Merline et al. 2013).

Other data sets reveal the existence of pairedbinaries/triples. Two such cases have been pub-lished: the pair composed of (3749) Balam and2009 BR60 (Vokrouhlicky 2009, and referencestherein) and the pair composed of (8306) Shoko

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and 2011 SR158 (Pravec et al. 2013). Balamis a confirmed triple, with a distant satellite de-tected by direct imaging (Merline et al. 2002a)and a close satellite detected by lightcurve obser-vations (Marchis et al. 2008d). Shoko is a sus-pected triple as well: Using lightcurve observa-tions, Pravec et al. (2013) detected an eclipsing,synchronous close satellite withPorb = 36.2 hand a third rotational component attributed to anouter satellite.

While the population of binary NEAs and smallMBAs is composed primarily of synchronoussystems, and secondarily of asynchronous sys-tems with low secondary-to-primary size ratios(Ds/Dp < 0.5), doubly synchronous binarieswith nearly equal-size components also exist(Fig. 4). Nine such systems withDs/Dp > 0.7and orbital periods between 15 h and 118 h havebeen reliably identified in the main belt (e.g.,Behrend et al. 2006; Kryszczynska et al. 2009,see also the Pravec and Harris binary databasedescribed above).

Another important observation is that, with theexception of doubly synchronous systems, all bi-naries have unelongated, near-spheroidal primaryshapes, as evidenced by their low primary am-plitudes not exceeding 0.3 mag (when correctedto zero phase angle). This suggests that theirprimaries may have shapes similar to the top-like shapes that have been observed for 1999KW4 (Ostro et al. 2006) and several other bina-ries by radar.

All the properties revealed by photometric ob-servations indicate that binary systems amongNEAs and small MBAs were formed from crit-ically spinning cohesionless parent bodies, withYORP as the predominant spin-up mechanism.This finding is consistent with the fact that theobserved 0.2–13 km size range of binaries cor-responds to the size range where the spin barrieragainst asteroid rotations faster than about 2.2 hhas been observed (e.g., Pravec et al. 2007).

Although lightcurve observations provide pow-erful constraints on binaries, there are limita-tions. Detection of mutual events requires anedge-on geometry and observations at the time ofthe events, such that some binaries remain unde-

Fig. 4.—Primary rotation period versus primary di-ameter. Groups A, B, and L are defined in the captionof Fig. 3. Three doubly synchronous asteroids withnearly equal-size components lie isolated in the plot:(69230) Hermes on the left and (90) Antiope and (617)Patroclus on the right of group B. Note that membersof group A cluster near the disruption spin limit forstrengthless bodies. Figure from Pravec and Harris(2007).

tected (e.g., (69230) Hermes during its 2003 ap-parition). Small satellites also escape detectionbecause their effect on the lightcurve is not mea-surable (e.g., satellites withDs/Dp . 0.17 re-main undetected if the minimum detectable rel-ative brightness attenuation is∼0.03 mag). Theprobability of mutual event detection is larger atsmaller semi-major axes (expressed in units ofprimary radius) and at larger size ratios, result-ing in observational biases (e.g., Pravec et al.2012). Finally, lightcurve observations yield rel-ative, not absolute, measurements of orbital sepa-rations. Detection of small or distant secondariesand direct measurement of orbital separation mustinstead rely on other observational techniques.

2.3 Lightcurve Observations of Asteroid Pairs

Vokrouhlicky and Nesvorny (2008) reportedevidence for pairs of MBAs with bodies in eachpair having nearly identical heliocentric orbits.Because chance associations can be ruled out,

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the asteroids in each pair must be genetically re-lated. Quantifying the difference in orbital pa-rameters is accomplished with a metricd thatcorresponds roughly to the relative velocity be-tween the bodies at close encounter. Vokrouh-licky and Nesvorny (2008) identified 44 asteroidpairs (excluding family members) with a distancebetween the orbits of their components amount-ing to d < 10 m/s. They showed that, when in-tegrated backwards in time, the orbits converge ata certain moment in the past with a physical dis-tance much less than the radius of the Hill sphereand with a low relative velocity on the order of1 m/s.

Pravec and Vokrouhlicky (2009) developed amethod to identify probable asteroid pairs by se-lecting candidate pairs with a similar distance cri-terion, then computing the probability that eachcandidate pair emerged as a result of a coinci-dence between two unrelated asteroids. Theyidentified 72 probable asteroid pairs, reproducingmost of the 44 previously known pairs. Most ofthe new candidates were later confirmed to be realpairs using backward integrations of their helio-centric orbits.

Vokrouhlicky and Nesvorny (2008) proposeda few possible formation mechanisms for the as-teroid pairs: collisional disruption, rotational fis-sion, and splitting of unstable asteroid binaries.Pravec et al. (2010) conducted a survey of therotational properties of asteroid pairs, and theyfound a strong correlation between the primaryrotational periods and the secondary-to-primarymass ratio (Fig. 5). They showed that this correla-tion fits precisely with the predictions of a modelby Scheeres (2007) in which a parent body withzero tensile strength undergoes rotational fission.The model predicts that primaries of low mass ra-tio pairs (q . 0.05) have not had their spin sub-stantially slowed down in the separation processand should rotate rapidly with frequencies closeto the fission spin rate. The observed periods arebetween 2.4 and 5 h. Primaries of medium massratio pairs (q = 0.05 to ∼ 0.2) have had theirspin slowed down according to the model becausea substantial amount of angular momentum wastaken away by the escaped secondary. This trend

Fig. 5.—Primary rotation periods versus mass ratiosof asteroid pairs. The mass ratio values were estimatedfrom the differences between the absolute magnitudesof the pair components,∆H. Circles are data pointswith quality code ratingUp = 3, meaning a preciseperiod determination. Diamonds are data points withUp = 2, which are somewhat less certain estimates.Error bars are one standard deviation. The data matchthe predictions (curves) of a model of rotational fissionwith a few adjustable parameters. In the model,Aini isthe binary system’s initial orbit semi-major axis,αL isthe normalized total angular momentum of the system(Fig. 3), andap, bp, cp are the long, intermediate, andshort axis of the dynamically equivalent equal massellipsoid of the primary. All models shown assumebp/cp = 1.2. The dashed curve shows the best-fitmodel withαL = 1.0, ap/bp = 1.4 andAini/bp = 3.Solid curves represent upper and lower limiting caseswith αL = 0.7−1.2. Figure updated from Pravec et al.(2010).

is observed in the data (Fig. 5). Finally, high massratio pairs withq > 0.2 should not exist, as thefree energy in the proto-binary system formed byrotational fission would be negative and the com-ponents would be unable to separate. Observa-tions mostly corroborate this prediction: all 32

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pairs in the sample of Pravec et al. (2010) werefound to have a mass ratio. 0.2. However, an ex-panded photometric survey with 64 asteroid pairsobserved between 2012 and the date of this writ-ing reveals 3 pairs with high mass ratio (q > 0.5).Their formation requires an additional supply ofangular momentum. Another important findingby Pravec et al. (2010) is that the primaries of as-teroid pairs have lightcurve amplitudes that im-ply shapes with a broad range of elongations, i.e.,unlike the primaries of binaries (Sections 2.1 and2.2), the primaries of asteroid pairs do not tend tobe nearly spheroidal.

2.4 Spectral Observations of Asteroid Pairs

Colorimetric and spectral observations of about20 asteroid pairs indicate that members of an as-teroid pair generally have similar spectra (Duddyet al. 2012; Moskovitz 2012; Duddy et al. 2013;Polishook et al. 2014a; Wolters et al. 2014). Insome pairs, the authors observed subtle spec-tral differences between the components and at-tributed them to a larger amount of weathered ma-terial on the surface of the primary. In two pairs,they observed somewhat more significant spec-tral differences. For the pair (17198)–(229056),both Duddy et al. (2013) and Wolters et al. (2014)found that the primary is redder, i.e., it has asomewhat higher spectral slope than the sec-ondary in the observed spectral range 0.5–0.9µm.It is unclear why their spectra differ despite astrong dynamical link between the two aster-oids. For the pair (19289)–(278067), Wolterset al. (2014) observed a spectral difference simi-lar to that seen in (17198)–(229056), but Duddyet al. (2013) observed very similar spectra. Cross-validation of the methods or additional observa-tions, perhaps rotationally resolved, are needed toresolve the discrepancy.

2.5 Direct Imaging of MBA and Trojan Sys-tems

Direct imaging of asteroids can reveal the pres-ence of satellites and, following the long traditionof orbit determination of binary stars and plan-etary satellites, lead to estimates of orbital pa-rameters (Fig. 6). This observing mode remains

challenging because the satellites are generallymuch smaller and fainter than their respective pri-maries and because most satellites known to dateorbit at angular separations below 1 arcsecond.Satellite discoveries have therefore followed thedevelopment of adaptive optics (AO), and recentadvances have enabled the detection of asteroidsatellites that had remained undetected in priorsearches.

Instruments must have sufficient contrast andresolving power to detect asteroid satellites withdirect imaging. For a 50–100 km diameter aster-oid in the main belt orbited by a satellite a fewkm across, the typical angular separation is gen-erally less than an arcsecond with a contrast of 5to 10 magnitudes (computed as 2.5log(Fp/Fs),whereF is the flux andp ands indicate primaryand secondary, respectively).

In some situations, direct images can actuallyresolve the primary. A 50–100 km diameter aster-oid at 2 au subtends 34–68 mas while the diffrac-tion limit of a 10 m telescope at a typical imag-ing wavelength of 1.2µm is about 30 mas. Al-though the diffraction limit is not reached, it canbe approached with high-performance AO instru-ments in excellent conditions. With a sequence ofdisk-resolved images that provide sufficient ori-entational coverage, it is possible to estimate the3D shape of the primary. This enables volumeand density determinations.

Instruments capable of meeting the contrastand resolution requirements include the Hub-ble Space Telescope (HST) and large (10 mclass) ground-based telescopes equipped withAO. Spacecraft encounters provide an opportu-nity to detect small satellites at small separationsbecause of proximity to the target and the ab-sence of the point spread function halo that affectsground-based AO instruments.

At the timeAsteroids III was published, MBAsatellite discoveries included one by spacecraft((243) Ida), one by HST ((107) Camilla), and 6by ground-based AO instruments. Since then,ground-based AO instruments have been respon-sible for almost all large MBA satellite discov-eries: (121) Hermione (Merline et al. 2002b),(379) Huenna (Margot 2003), (130) Elektra

10

Fig. 6.— Satellite detection by direct imaging with adaptive optics(AO). (a) Image of asteroid (41) Daphne(Vmag=10) obtained with a ground-based AO-fed camera (NACOat ESO VLT, 5 s exposure). (b) Same imageafter subtraction of the flux from the primary, enabling moreaccurate measurements of the flux and position ofthe secondary. (c) Orbit determination. The relative positions of the satellite from VLT/NACO and Keck/NIRC2images are indicated. Figure adapted from Carry (2009).

(Merline et al. 2003c), a second satellite to (87)Sylvia (Marchis et al. 2005b) and to (45) Euge-nia (Marchis et al. 2007), (702) Alauda (Rojo andMargot 2007), (41) Daphne (Conrad et al. 2008),two satellites to (216) Kleopatra (Marchis et al.2008b) and (93) Minerva (Marchis et al. 2009),and (317) Roxane (Merline et al. 2009). The widebinaries (1509) Esclangona (Merline et al. 2003a)and (4674) Pauling (Merline et al. 2004), whichare small asteroids in our classification, have alsobeen identified using AO-fed cameras. HST en-abled detections of two additional wide binaries:(22899) 1999 TO14 (Merline et al. 2003b) and(17246) 2000 GL74 (Tamblyn et al. 2004), both ofwhich are small MBAs. No satellites have beendiscovered around any of the 7 asteroids recentlyvisited by spacecraft: (4) Vesta, (21) Lutetia,(2867)Steins, (4179) Toutatis, (5535) Annefrank,(25143) Itokawa, and (132524) APL. The num-ber of known large MBAs with satellites is now16, which includes the only known large dou-bly synchronous system, (90) Antiope (Merlineet al. 2000; Michałowski et al. 2004; Descampset al. 2007, 2009). The fraction of large MBAswith satellites is difficult to estimate because ofa complex dependence of satellite detectabilityon primary-to-secondary angular separation andprimary-to-secondary flux ratio. However, be-cause several independent programs have sur-

veyed over 300 large MBAs, it is likely that theabundance of binaries in large MBAs is substan-tially smaller than the∼16% abundance in NEAsand small MBAs.

Properties of large MBA binaries and triplesare summarized in Figs. 7 and 8. With the excep-tion of the nearly equal-mass binary (90) Antiope,the known satellites have secondary-to-primarymass ratios between 10−6 and 10−2. All haveorbital periods between 1 and 5.5 days, except(379) Huenna, whose orbit has a period of∼88days and an eccentricity of∼0.2 (Marchis et al.2008c). Many orbits have near-zero eccentric-ity (e.g., Marchis et al. 2008a), likely the resultof tidal damping, but the inner satellites of triplesgenerally have non-zero eccentricities. Theseeccentricities may have originated when orbitscrossed mean motion resonances while tidally ex-panding (e.g., Fang et al. 2012).

At first glance, large MBA densities appear tocluster in two groups, between 1 and 2 g/cm3 andabove 3 g/cm3. However, interpretations are lim-ited by the possibility of systematic errors, in-cluding overestimates of volumes and underesti-mates of densities (Pravec and Harris 2007). Be-cause volume uncertainties almost always dom-inate the error budget for binary asteroid densi-ties (e.g., Merline et al. 2002c; Carry 2012), it isimportant to assess the realism of uncertainties

11

1016

1017

1018

1019

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50

100

150

200

250

300

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)

0.00.51.01.52.02.53.03.54.0

De

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ty (

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)

87

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7 C

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Fig. 7.— Properties of large MBA binaries andtriples, excluding the doubly synchronous (90) An-tiope. Error bars or upper limits, when available, areshown. Figures 7 and 8 are based on data compiledby Johnston (2014) from references therein.

10-6

10-5

10-4

10-3

10-2

Mass ratio

1.01.52.02.53.03.54.04.55.05.5

Orbital Period (d)

200

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1200

1400Semi-major Axis (km

)

87 Sylvia (I)

87 Sylvia (II)

107 Camilla (I)

22 Kalliope (I)

130 Elektra (I)

41 Daphne (I)

702 Alauda (I)

45 Eugenia (I)

45 Eugenia (II)

121 Herm

ione (I)

216 Kleopatra (I)

216 Kleopatra (II)

93 Minerva (I)

93 Minerva (II)

762 Pulcova (I)

283 Emma (I)

0.000.020.040.060.080.100.120.140.160.18

Eccentricity

Fig. 8.—Properties of satellites of large MBAs, ex-cluding outliers (90) Antiope and (379) Huenna (seetext). Satellites of (243) Ida and (317) Roxane, whoseorbits are not well known, are not shown.

12

associated with volume determinations. Somepublished density values should be regarded withcaution because overconfidence in the fractionaluncertainty of volume estimates has led to un-derestimates of bulk density uncertainties. Theplatinum standard of an orbiting spacecraft yieldsdensities with∼1% accuracy. The gold standardof radar observations where tens of images withhundreds or thousands of pixels per image areused to reconstruct a detailed 3D shape modelyields volumes (and densities) with∼10% accu-racy. In contrast, AO images contain at most a fewindependent resolution cells of the target aster-oid. Shape reconstructions based on AO imagesand/or lightcurve data may not routinely yieldvolume accuracies at the 10% level, although oneanalysis reached that level (Carry et al. 2012). Inthe absence of precise volume information, onemight be tempted to infer bulk densities fromthe theory of fluid equilibrium shapes, but thisapproach is problematic (Holsapple 2007; Harriset al. 2009).

In the Jupiter trojan population, one satelliteto (624) Hektor has been reported (Marchis et al.2006b) since the discovery of the first trojan satel-lite to (617) Patroclus (Merline et al. 2001). Theseare the only trojans confirmed to have satellitesin spite of several active search programs. Theapparent low abundance of binary trojans is in-triguing and, if confirmed, may provide addi-tional support for the idea that Jupiter trojansoriginated in the trans-Neptunian region (Mor-bidelli et al. 2005; Levison et al. 2009) wherethey experienced a different collisional environ-ment than in the main belt of asteroids. (624)Hektor has a satellite in a∼3-day orbit that is ec-centric (∼0.3) and inclined (∼50◦) with respect toHektor’s equator (Marchis et al. 2014). (617) Pa-troclus is unusual because it has two componentsof similar size in a relatively tight (∼680 km) or-bit, with a normalized total angular momentumexceeding that available from fission of a singleparent body (Marchis et al. 2006a).

In the trans-Neptunian region, 14 and 64 binarysystems have been discovered with AO and HST,respectively (Johnston 2014). The apparent largerabundance of binary TNOs in the cold classical

belt may be due to a different dynamical environ-ment and formation mechanism (Section 5).

Objects in the trojan and TNO populations aregenerally too faint for AO observations in naturalguide star (NGS) mode, in which the science tar-get is also used to measure the properties of thewavefront and command the deformable mirror.These objects can be observed in appulse whentheir sky position happens to be within. 1 ar-cminute of a bright star. The advent of laser guidestar (LGS) adaptive optics has been an impor-tant development that has freed the observer fromfinding such chance alignments and has openedup a larger fraction of the sky for observation offaint objects. Even with LGS, however, the avail-ability of a tip-tilt star (Rmag. 18) within . 1arcminute of the target is still required.

High-resolution and high-contrast imagingcapabilities are aggressively sought by instru-ment builders, in part to enable direct imagingof exoplanets. Cameras equipped with high-performance AO are currently being installedor commissioned on large ground-based tele-scopes: HiCIAO on Subaru, GPI on Gemini, andSPHERE at the ESO VLT. These instruments willimprove the ability to detect faint satellites orbit-ing close to their respective primaries. However,in most cases, asteroids fall in the faint-end rangeof these instrument capabilities. The next gener-ation of large telescopes (∼30 m diameter) suchas the Thirty Meter Telescope (TMT) and Eu-ropean Extremely Large Telescope (E-ELT) willprovide an improvement in sensitivity by a factorof ∼10 and in angular resolution by a factor of∼3 compared to current 10 m telescopes. Withthe anticipated development of AO capabilities atshorter wavelengths, the second generation of in-struments at these facilities is expected to provideimprovements in angular resolution by a factor of∼5. Such instruments may allow detection of thesmall MBA binaries that are currently beyond thereach of direct imaging instruments. In many ofthese systems, the components are separated byonly a few mas and the size ratios are larger thanin large MBA binaries, resulting in flux ratioscloser to unity.

13

2.6 Spectral Observations of MBA and TrojanSystems

It is generally difficult to separate the lightemitted or reflected from the secondary from thatof the brighter primary. Nevertheless, such ob-servations can be attempted when the secondaryhappens to be at a large angular separation fromthe primary, when the system is undergoing mu-tual events, or with the help of an integral fieldspectrograph.

Spectra of (22) Kalliope and its satellite Li-nus in the 1–2.4µm region appear to be sim-ilar (Laver et al. 2009), which the authors at-tribute to satellite formation after a major impacton the precursor body. Observations of both com-ponents of (90) Antiope in the same spectral re-gion also shows surface reflectances that are sim-ilar (Marchis et al. 2011). The spectrum of (379)Huenna is characteristic of C-type asteroids andthe secondary does not exhibit a significantly dif-ferent taxonomic type (DeMeo et al. 2011). Bothcomponents of (809) Lundia are consistent with aV-type classification (Birlan et al. 2014).

In the mid-infrared, Spitzer observations of thetrojan (617) Patroclus, including during mutualevents, provided size estimates for its componentsand a thermal inertia of 20± 15 J s−1/2 K−1 m−2

(Mueller et al. 2010). Spitzer observations com-bined with photometric results in the visibleyielded size and albedo estimates for (624) Hek-tor (Emery et al. 2006). Spitzer observations ofthese and other binaries did not resolve the bina-ries and results typically cannot be compared toobservations that place many resolution elementson individual components. One exception is2000 DP107, where analysis of Spitzer data yieldsa system density of0.9 ± 0.3 g/cm3 (Marchiset al. 2012) and the radar results indicate1.4 ±

0.2 g/cm3 (Naidu et al. 2015).

2.7 Stellar Occultations of MBA and TrojanSystems

Stellar occultations provide a way of detect-ing components of a multiple-asteroid system, ofplacing bounds on component sizes, and of ob-taining the relative positions of components on

the plane of the sky. A recording of star light asa function of time shows a deep extinction whena target body crosses the line of sight between theobserver and the star. This can be interpreted interms of achord on the apparent disk of the tar-get body projected on the plane of the sky. Ifseveral observers are placed across the occulta-tion path on the surface of the Earth, multiplechords can be obtained, and the size and shapeof the target projected on the sky can be recon-structed (Fig. 9). When two or more componentsare present, it is also possible to measure their rel-ative position. While the reliability of this tech-nique was disputed a decade ago due to the lackof digital recordings, the availability of low-costcameras and global positioning systems has en-abled a dramatic improvement in the precision oftiming reports. Stellar occultations have becomean important observational tool for the study ofbinary asteroids.

Early reports (e.g., Binzel and van Flandern1979) of asteroids suspected to be binaries on thebasis of occultation data (including (3) Juno, (6)Hebe, (9) Metis, (12) Victoria, (18) Melpomene,(146) Lucina, and (532) Herculina) have re-mained largely unconfirmed despite extensivefollow-up searches. However, it is likely thatthe outer satellite of (216) Kleopatra was de-tected during a 1980 occultation (Dunham 1981;Descamps et al. 2011). The detection of a satel-lite around the trojan (911) Agamemnon has beensuggested (Timerson et al. 2013) but not yet con-firmed. The occultation technique has also beenused to detect rings around the centaur (10199)Chariklo (Braga-Ribas et al. 2014).

One strength of the stellar occultation tech-nique lies in the fact that the observability of theevent depends mainly on the brightness of the starand not of the asteroid or satellite. Stellar occul-tations can thus be used to detect small (km size)satellites, even those that are close to the primaryand that would remain undetected in direct imag-ing.

Another strength of the technique is the po-tential for high-precision measurements. Stellaroccultations are based on time-series photometry.Given a sufficiently high cadence (e.g., 10–30 im-

14

ages per second), it is possible to obtain a preci-sion of a few mas on the relative position of bi-nary components, which is 5 to 10 times betterthan with direct imaging with current instrumen-tation.

Finally, well-sampled stellar occultations al-low for recovery of the size and apparent shapeof asteroids and their satellites, whereas opticallightcurves and direct imaging observations pro-vide primarily the diameter ratio of the compo-nents and more limited shape information. So far,four successful observations of satellite size andshape have been reported: Linus, satellite of (22)Kalliope (Descamps et al. 2008), Romulus, theouter satellite of (87) Sylvia (Berthier et al. 2014),and both components of the equal-size binaries(90) Antiope (Bartczak et al. 2014) and (617) Pa-troclus (Buie et al. 2014).

Fig. 9.— The apparent shape of Linus, a satelliteof (22) Kalliope (Margot and Brown 2003), detectedby stellar occultations. In this analysis, the profile ofthe satellite (solid curve) fitted to the observed chords(straight lines) yields an equivalent diameter of 30±

6 km. Dashed curves show the corresponding uncer-tainty of the fitted profile, and dashed lines show neg-ative detections. Figure adapted from Descamps et al.(2008).

Despite all of these strengths, there remains arelatively low number of well-covered stellar oc-cultation events. This is due, in part, to the re-quirement of successful observations at many sta-tions. Owing to uncertainties on both the starand asteroid positions, the occultation path can

shift by several tens or even hundreds of km onEarth compared to the prediction. Observers musttherefore spread geographically to cover an event,but the detection of a satellite by several stationsrequires a fine grid of observers.

The situation is, however, expected to improvedramatically with the availability of the Gaia stel-lar catalog and better asteroid orbits (Tanga andDelbo 2007). Predictions of the occultation paths(for the center of mass) will be accurate to a fewkm, and the main source of uncertainty will be-come the prediction of the relative position of thesatellite around the primary.

2.8 Other Observations

There have been several attempts to use ground-based interferometers to measure the angular sep-aration of binary systems (Delbo et al. 2009;Carry et al. 2015). However, asteroid satellitesare too faint for current interferometers operatingin the visible and near-infrared and at the edge ofdetection in the mid-infrared. Future instrumen-tation may allow such observations. There arealso prospects for observations with the ALMAsub-millimeter array (Busch 2009).

3. DYNAMICS

In parallel with advances in instrumentationand observing capabilities, the field has seentremendous developments in understanding thedynamical processes that affect asteroid systems.This has been enabled in large part by the avail-ability of detailed shape models and orbital pa-rameters, by the need to model the dynamics ofnewly discovered triple systems, and by the desireto understand formation and evolution processes.

A non-exhaustive list of some dynamical prob-lems that have been explored sinceAsteroids IIIincludes the stability of asteroid satellite orbits(Scheeres 2002; Frouard and Compere 2012),the dynamics around triaxial bodies (Scheeres2009a), the fate of asteroid ejecta (Scheeres2007), the formation of contact binaries via dy-namical evolution (Scheeres 2009a; Taylor andMargot 2011, 2014), the genesis of eccentric andmutually inclined orbits (Fang et al. 2011; Fang

15

and Margot 2012c), the orbital determination oftriple systems using point-mass approximations(Marchis et al. 2010) and full N-body calcula-tions (Fang et al. 2012), the influence of Kozaicycles on binaries (Perets and Naoz 2009; Fangand Margot 2012b), the effects of close planetaryencounters on mutual orbits (Fang and Margot2012a) and spin states (Takahashi et al. 2013),the complex spin-orbit interactions with irreg-ular component shapes (Scheeres et al. 2006),including the libration and irregular rotation ofsecondaries (Naidu and Margot 2015), the in-fluence of internal structure (Goldreich and Sari2009), material properties (Taylor and Margot2011) and nonspherical shapes (Taylor and Mar-got 2014) on tidal evolution, the possibility oftidal saltation (Harris et al. 2009; Fahnestockand Scheeres 2009), the possibility of significantradiative evolution (Cuk and Burns 2005;Cuk2007; Cuk and Nesvorny 2010; McMahon andScheeres 2010a,b), and the possibility of a stableequilibrium between tidal and radiative evolution(Jacobson and Scheeres 2011a).

Several radar data sets provide exquisite con-straints for dynamical studies. Reflex motionhas been measured for 2000 DP107 (Margot et al.2002; Naidu et al. 2015), 1999 KW4 (Ostro et al.2006), and 1991 VH (Naidu et al. 2012), allow-ing masses of individual components to be de-termined. Because detailed component shapesare also available, one can fully model the sys-tem dynamics and study spin-orbit coupling indetail (Scheeres et al. 2006; Fahnestock andScheeres 2008; Naidu and Margot 2015). Onefinding from this work is that even moderatelyelongated secondaries on mildly eccentric or-bits are likely to experience chaotic rotation thatsubstantially affect binary evolution timescales(Fig. 10).

4. SMALL ASTEROIDS: SYNTHESIS

4.1. Rotational Fission Hypothesis

With the exception of the doubly synchronousbinary asteroid systems, the primary asteroidsof all small binary systems are rapidly rotating

Fig. 10.—Surface of section plot showing the pos-sible rotational regimes of the∼200 m secondary of1991 VH (secondary elongationa/b = 1.5 and mu-tual orbit eccentricitye = 0.05). The plot shows theangle between the long axis and the line of apsidesof the mutual orbit,θp, against its time derivative,θp, normalized by the mean motion,n, at each peri-center passage. Five trajectories are illustrated (fromtop to bottom: non-resonant quasi-periodic, periodic,chaotic, periodic, periodic). While trapped in the seaof chaos, the secondary experiences torques on its per-manent deformation that result in a highly variablespin rate, preventing BYORP-type evolution. Figurefrom Naidu and Margot (2015).

(within a factor of only a few of the critical dis-ruption spin limit for bodies with no shear or ten-sile strengthωd =

√

4πρG/3). Furthermore, al-most all known small binary asteroids have highangular momentum contents (Pravec and Har-ris 2007). These characteristics are not consis-tent with formation following a sub-catastrophicimpact, capture through a three-body interactionin the near-Earth or main belt, or capture af-ter a catastrophic impact. Instead, they are in-dicative of formation from a rotational fissionevent (e.g., Margot et al. 2002; Pravec and Har-ris 2007). The rotational fission hypothesis positsthat a parent asteroid can be torqued to a rota-tion rate so great that the centrifugal accelerationsoverpower the gravitational accelerations holdinga strengthless asteroid together (Weidenschilling1980). It is possible that some small asteroidshave cohesive or molecular strength in addition

16

to self-gravity (e.g., Rozitis et al. 2014). In thesecases, the centrifugal accelerations must over-come these additional forces in order for the as-teroid to fission (Pravec and Harris 2000; Sanchezand Scheeres 2014). At rapid rotation rates, loosesurface material can flow from high-latitude re-gions to the equator along potential gradients (Os-tro et al. 2006). It has been shown that rota-tional acceleration could trigger local slope fail-ures and landslides, which can form the canon-ical top shape and equatorial bulge seen on pri-mary components in small multiple-asteroid sys-tems (Walsh et al. 2008; Harris et al. 2009).

Bottke et al. (2002) proposed a YORP-inducedrotational fission hypothesis. It has since beenshown that the YORP effect controls the ro-tational acceleration of small asteroids (Bottkeet al. 2006; Marzari et al. 2011) and naturallyexplains the period distribution among small as-teroids (Pravec et al. 2008; Rossi et al. 2009; Pol-ishook and Brosch 2009). Furthermore, includingthe YORP-induced rotational fission hypothesisin size-frequency distribution models improvesthe agreement with observations (Jacobson et al.2014a). The observed characteristics of the sys-tems described in Sections 2.1-2.3 as well as ther-mal inertia observations (Delbo et al. 2011) areconsistent with a binary formation mechanismthat involves spin-up and mass shedding. TheYORP-induced rotational fission hypothesis is theleading candidate for explaining the formation ofbinaries, triples, and pairs among small asteroids.

4.2. Asteroid Pairs

The YORP effect can increase the spin rate ofasteroids beyond the critical disruption spin limit,thereby triggering rotational fission. In actuality,there is some uncertainty regarding the spin rateat which disruption occurs—there may be failureand deformation before fission (Walsh et al. 2008;Sanchez and Scheeres 2011; Cotto-Figueroa et al.2013). The critical disruption spin limit also de-pends on the detailed shapes, masses, interlock-ing nature of the interior components and anycohesive forces (Scheeres 2007, 2009b; Sanchezand Scheeres 2014). Despite ignoring these de-tails, simple calculations provide a rotational fis-

sion model that can be compared directly and suc-cessfully with observations.

If a spherical approximation of each compo-nent is made, then the rotational breakup spinrateωq necessary for fission as a function of thesecondary-to-primary mass ratioq is (Scheeres2007):

ωq = ωd

√

1 + q

(1 + q1/3)3. (1)

This is the exact solution for two spheres restingon each other with a mass ratio ofq and rotatingabout the axis of maximum moment of inertia.

The spherical component model describedabove demonstrates the important reality that thelarger the mass ratioq of the two future binarymembers, the slower the required rotation ratenecessary to create the binary system. This slowerrequired rotation rate translates into a small initialfree energy for the ensuing binary system. Thefree energyEf is the energy that is accessible tothe different energy reservoirs in the system, in-cluding the rotation states of each member andthe orbit. It does not include the internal bind-ing energy of each object. The free energy isan important quantity because it determines theboundedness of the system. Bound systems havenegative free energy, while unbound systems havepositive free energy. An unbound binary systemimplies that the system is capable of disruptionbut does not imply that the system will disrupt.For the idealized case of two spheres, the freeenergy can be expressed as (Scheeres 2007):

Ef =2πρω2

dR5p

15f(q), (2)

whereRp is the radius of the primary andf(q) isan algebraic, monotonically decreasing functionfor 0 < q ≤ 1. For the equation above corre-sponding to two spheres, the function crosses zerowhenq ≈ 0.204. Similar equations can be writtenfor any two component shapes, butq ∼ 0.2 re-mains near the binding energy transition point, sothe model uses this point as a simple approxima-tion. This crossing point divides bound systemswith negative energy and mass ratiosq > 0.2and unbound systems with positive energy and

17

mass ratiosq < 0.2. Because of this fundamen-tal difference, high mass ratioq > 0.2 and lowmass ratioq < 0.2 binary systems evolve dif-ferently (Scheeres 2009a; Jacobson and Scheeres2011b). Primarily, positive energy low mass ra-tio systems will chaotically explore orbital phasespace until the majority find a disruption trajec-tory creating an asteroid pair; this evolutionaryroute is unavailable to high mass ratio systems.

The asteroid pair population provides a natu-ral laboratory to test this relationship (Scheeres2007; Vokrouhlicky and Nesvorny 2008). Pravecet al. (2010) examined many asteroid pair sys-tems and measured the rotation rate of the pri-mary and the absolute magnitude difference be-tween the pair members. These two quantitiesshould follow a simple relationship related toωq,although many of the ignored details mentionedat the beginning of this section can move aster-oids away from this relationship. Indeed, Pravecet al. (2010) discovered that asteroid pairs do fol-low this relationship (Fig. 5). Furthermore, theyfound that the large members of asteroid pairshave a broader range of elongations than the pri-maries of binary systems, consistent with the find-ings of Jacobson and Scheeres (2011b) that pro-late primaries are less likely to remain in a boundbinary system after rotational fission. Thus, thereis strong evidence to support the hypothesis thatasteroid pairs are the products of rotational fis-sion.

Asteroid pairs continue to be a fertile obser-vational landscape. Since dynamical integrationscan derive the “birthdate” of such systems, ob-servers can test ideas regarding space weatheringtimescales and YORP evolution after fission (Pol-ishook et al. 2014a; Polishook 2014). Along withbinary systems, the surfaces of asteroid pairs mayprovide clues in the future regarding the violenceof the rotational fission process (Polishook et al.2014b).

4.3. Binary and Triple Systems

Jacobson and Scheeres (2011b) showed that af-ter rotational fission there are a number of possi-ble outcomes. Their numerical studies producedthe evolutionary flow chart shown in Fig. 11;

many of these outcomes were also found by Fangand Margot (2012c). The high and low mass ra-tio distinction for rotational fission emphasizedabove plays an important role in distinguishingthe two evolutionary pathways. Along the highmass ratio pathway, both binary members tidallysynchronize and then evolve according to the BY-ORP effect.

Along the low mass ratio pathway, the bi-nary system is unbound. Since these systems arechaotic, many are disrupted and become aster-oid pairs. During this chaotic binary state, thesecondary can often go through rotational fissionitself, although this rotational fission is torquedby spin-orbit coupling (Fig. 10) rather than theYORP effect. Loss of material from the sec-ondary stabilizes the remaining orbiting compo-nents. The lost mass may reaccrete onto the pri-mary, perhaps contributing to the observed equa-torial ridges, or may escape from the system. Inthese cases, the system undergoes another chaoticbinary episode with three possible outcomes: are-shaped asteroid, an asteroid pair, or a stablebinary. These binaries still possess positive freeenergy such that they may disrupt if disturbed. Inother cases, the system retains three componentsafter secondary fission. While the numerical sim-ulations of Jacobson and Scheeres (2011b) didnot yield this latter outcome, it is possible thatthis pathway explains the existence of stable triplesystems.

After stabilization of the low mass ratio bi-nary system, the secondary synchronizes due totides (e.g., Goldreich and Sari 2009), althoughsome satellites may be trapped in a chaotic ro-tation state for durations that exceed the classicspin synchronization timescales (Naidu and Mar-got 2015). Then the system evolves according tothe BYORP effect and tides. These binary evo-lutionary processes and their outcomes are dis-cussed in Walsh & Jacobson (this volume). Asshown in Fig. 11, these evolutionary paths includeeach of the binary morphologies identified in thischapter and by other teams (Pravec and Harris2007; Fang and Margot 2012c). In particular, theformation of wide asynchronous binaries such as(1509) Esclangona, (4674) Pauling, (17246) 2000

18

Fig. 11.— Flowchart showing the possible evolutionary paths for an asteroid after it undergoes rotationalfission. Each arrow is labeled with the dominant process and an estimated timescale for this process. Underlinedstates are nominally stable for a YORP effect timescale. Figure from Jacobson and Scheeres (2011b).

GL74, and (22899) 1999 TO14 is best explained bya rotational fission mechanism (Polishook et al.2011) followed by BYORP orbital expansion (Ja-cobson et al. 2014b).

An alternative formation mechanism for triplessuch as (153591) 2001 SN263 and (136617) 1994CC is that after creating a stable binary system,the primary undergoes rotational fission a secondtime. As long as the third component is on a dis-tant enough orbit, then this process may result ina stable triple system (Fang et al. 2011; Fang andMargot 2012c; Jacobson et al. 2014b).

5. LARGE ASTEROIDS: SYNTHESIS

The primaries of most known binary and tripleasteroids greater than 20 km have spin periods inthe range of 4 h to 7 h (Fig. 7). While these spinrates are not near the disruption spin limit, theyare typically faster than the mean spin rates for as-teroids of similar sizes. The total angular momen-tum content, however, is well below that requiredfor rotational fission. The secondary-to-primarymass ratios in these systems range from 10−6 to10−2. These properties are consistent with satel-

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lite formation during large collisions (Fig. 12).Durda et al. (2004) have shown in numerical sim-ulations that impacts of 10- to 30-km diameterprojectiles striking at impact velocities between3 kms−1 and 7 kms−1 can produce satellites thatmatch observed properties. Multiple asteroid sys-tems, e.g., (45) Eugenia (Merline et al. 1999;Marchis et al. 2007) and (87) Sylvia (Margot andBrown 2001; Marchis et al. 2005a) can also plau-sibly form through collisions.

Fig. 12.—Numerical simulations show that binariescan form as a result of large impacts between asteroids.In some scenarios, impact debris can remain gravita-tionally bound to the target body, forming a satellite(SMATs). This process likely explains the formationof large MBA binaries. In other scenarios, two frag-ments from the escaping ejecta have sufficiently sim-ilar trajectories, such that they become bound to oneanother (EEBs). Figure from Durda et al. (2004).

There is more uncertainty related to the forma-tion of (90) Antiope and (617) Patroclus, whichare both too large to be substantially affected byYORP. Hypotheses for the formation of (90) An-tiope include primordial fission due to excessiveangular momentum (Pravec and Harris 2007), animprobable low-velocity collision of a large im-pactor (Weidenschilling et al. 2001), or shrinkingof an initially wide binary formed by gravitationalcollapse (Nesvorny et al. 2010). Gravitationalcollapse in a gas-rich protoplanetary disk hasbeen invoked to explain the formation of numer-ous binaries in the trans-Neptunian region. (617)Patroclus may be a primordial TNO that avoideddisruption during emplacement in the trojan re-

gion (Nesvorny et al. 2010). Wide TNO binarieswould not be expected to survive this process,whereas encounter calculations (e.g., Fang andMargot 2012a) show that tight binaries would.

6. CONCLUSIONS

Studies of binaries, triples, and pairs remaina fertile ground for observing processes that areimportant in planet formation and for measur-ing quantities that are difficult to obtain by othermeans. These include masses and densities aswell as thermal, mechanical, and interior proper-ties. Binaries or triples have been found in∼50NEAs,∼50 small MBAs,∼20 large MBAs, and2 trojans. A unifying paradigm based on rota-tional fission and post-fission dynamics explainsthe formation of small binaries, triples, and pairs.Because the sun-powered rotational fission pro-cess is unrelenting, and because the productionof pairs is a frequent outcome of this process, asubstantial fraction of small bodies likely origi-nated in a rotational disruption event. This originaffects the size distribution of asteroids and mayexplain the presence of single NEAs with equa-torial bulges observed with radar. Small satel-lites of large MBAs are likely formed during largecollisions. Advances in instrumentation, observa-tional programs, and analysis techniques hold thepromise of exciting findings in the next decade.

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